The present invention relates to the magnetic resonance art. It finds particular application in three dimensional or volumetric imaging and will be described with particular reference thereto, although the benefits may be equally applicable to two or four dimensional imaging. It is to be appreciated, however, that the invention may also find application in other imaging and spectroscopy techniques in which a partial or incomplete data set is reconstructed.
Heretofore, medical diagnostic magnetic resonance imaging has included the sequential pulsing of radio frequency signals and magnetic field gradients throughout an examination region to be imaged. In volumetric or three dimensional imaging, a region of interest of a patient is disposed in a substantially uniform, main magnetic field. An RF excitation pulse is applied to tip at least some of the magnetization aligned with the field into a transverse plane. The RRF excitation may be applied independent of a gradient or concurrently with a slice select gradient. A primary phase encode gradient is applied along one direction and a secondary phase encode gradient is applied along another direction which may also be the slice select gradient direction. In each repetition of the pulse sequence, one of the phase encode gradients is stepped at regular intervals from a negative maximum phase encode gradient, through a zero phase encode gradient, to a positive maximum phase encode gradient. For each gradient step of the first phase encode gradient, the other phase encode gradient is similarly stepped at regular intervals from the negative maximum, through zero, to the positive maximum. Commonly, an RF pulse and/or a gradient field is applied to manipulate the magnetization to cause an ensuing magnetic resonance echo. During the echo, a read gradient is applied along a third direction and echo data is sampled. Typically, the set of data points sampled during an echo is termed a view or step. The complete set of views or steps are operated on with a three dimensional Fourier transform to generate a resultant three dimensional image representation.
Each datum or element of the three dimensional, (3D), or volume data set can be thought of as a sample of a single point in k-space. In this representation, k corresponds to a 3D spatial frequency. Its projection in the phase encode direction caused by the phase encode gradients is equivalent to its projection in the read direction caused by the read gradient. When the sampling of k-space is done in an isotropic manner, each point in the data set is related to another point by the conjugate symmetry relation: EQU F(k)=F*(-k)
In practice, this symmetry relationship is subverted by unpredictable phase variations that result from sequence and magnetic field considerations. Thus, conventionally, a full data set is acquired, 3D Fourier transformed, and the magnitude of the complex result taken to render an image that is phase independent.
In traditional three dimensional imaging, the phase encode gradients might each vary in equal increments with 128 steps and 128 data points might be sampled in each view, defining a volume in k-space that is 128.sup.3 complex values. If each magnetic resonance excitation, phase encode, and echo sample sequence is repeated every 100 msec. and two repetitions of each encoding are averaged, a total scan time of almost an hour is required. With human patients, scan times of this duration are often undesirable. Moreover, long scan times limit three dimensional imaging to substantially motion-free areas of the anatomy, such as brain scans.
Various ways of reducing the scan time have been proposed. The repeat time cannot be reduced without loss of signal because it takes a finite time to regrow longitudinal magnetization between repetitions of the pulse sequence. Likewise, a reduction in echo time affects the image contrast. Scan time may be reduced by simply taking fewer steps in one of the phase encoding directions. This, however, may result in resolution loss and/or aliasing problems. One way to reduce the acquisition time is to define a thick slice in one of the phase encoding directions, then do the volume within this slice. Since there is effectively no object outside the slice, one can increase the spacing between phase encode views to reduce the number of views taken in the slice direction without affecting resolution. Unfortunately, because of imperfections in the slice definition, images from slices near the edges may not be acceptable.
Another method for reducing scan time is to increase the number of data points sampled per scan, such as the technique shown in U.S. Pat. No. 4,678,996. Others have reconstructed two dimensional images using only half a set of views, i.e. only the positive views or only the negative views.
The present invention provides a new and improved technique for reconstructing volumetric images with less than a full set of data and which compensates for the above referenced problems and others.